The term for the medical procedure in which a baby is delivered through an incision in the mother’s abdomen is spelled and written several different ways.
In general usage, the initial c in Caesarean section is sometimes capitalized and sometimes not. This is a matter of editorial preference. In the U.S. and Canada, the capitalized form prevails. In the U.K. and elsewhere outside North America, the uncapitalized form is more common. Whether capitalized or not, caesarean (with two e‘s) is the usual spelling, though caesarian (one e, one i) is also common and has historically had periods of prevalence.
There are also cesarian and cesarean. The latter is standard in medical usage, appearing (in Google’s Scholar index) approximately three times for every instance of caesarean, the second-most common form. In medical writing, the term is usually uncapitalized.